I have the following problem:
- I have a given polygon (any shape)
- I have a grid with given size of grid cells (variable width and height)
- The grid contains the polygon (various number of cells required)
I know the following inputs:
- number of grid cells to contain the polygon (rows, columns)
- the number of required full cells and partial cells (that are fully inside or partially intersected with the polygon)
- the length of each side of the polygon
- the angle at each corner (between each side)
I need to calculate how many intersections there are in the polygon.
A few example by pictures (I need to know the number of the gray circles):
If you need more clarification, tell me.
Do you have any hint of what kind of formula could count the number of the intersections?